1. Technical Field
The present invention relates to a Lamb-wave high-frequency resonator, and in particular, it relates to a Lamb-wave high-frequency resonator including a quartz substrate and an interdigital transducer (IDT) electrode, the cut angle of the quartz substrate and the direction of propagation of Lamb wave being expressed in Euler angles (0, θ, 0).
2. Related Art
Typical high-frequency resonators include surface acoustic wave devices using a Rayleigh wave or an SH wave and a Lamb-wave resonator using a Lamb wave. As the substrates for them, an ST-cut quartz for a Rayleigh wave and an STW-cut quartz for an SH wave are adopted: for high-frequency resonators using a Lamb wave, an AT-cut quartz is used.
For example, it is known to use a Rayleigh-wave surface acoustic wave device in which an IDT electrode is formed along the Z′ axis on the surface of a quartz substrate called an ST-cut quartz (e.g., refer to Nonpatent Document 1: Kanna, S., “Analysis of Frequency-Temperature Characteristic of Surface Acoustic Wave Using Finite Element Method) Technical Report of IEICE, US99-20 (199-06), pp. 37-42).
It is also known to use an SH-wave surface acoustic wave device that propagates a transverse wave in an STW-cut quartz, that is, the direction of propagation of a surface acoustic wave is shifted 90 degrees relative to the ST-cut quartz. (e.g., Patent Document 1: JP-A-10-233645, pp 3-6, FIG. 1).
It is also known to use a Lamb-wave high-frequency resonator using a Lamb wave in which an IDT electrode is formed on the surface of an AT-cut quartz substrate, which propagates a bulk wave in the quartz substrate such that it is repeatedly reflected by the upper and lower surface thereof, and in which the thickness H of the quartz substrate and the wavelength λ of the Lamb wave are expressed as 0<2H/λ≦10 (e.g., refer to Nonpatent Document 2: Nakagawa, Y., Momose, M., Kakio, S., “Lamb-Wave Surface Acoustic Wave Device Substrate” 33th EM symposium 2004, pp. 93-96 and Patent Document 2: JP-A-2003-258596)).
According to Nonpatent Document 1, the frequency variation with temperature is about 140 ppm in a temperature range from −40° C. to 90° C., exhibiting an excellent frequency temperature characteristic as a surface acoustic wave device, but it is not sufficient as a resonator for which high accuracy is required. This surface acoustic wave device has a theoretical phase velocity of about 3100 m/s, which is difficult to provide for high-frequency bands.
The surface acoustic wave device according to Patent Document 1 is an end-reflecting surface wave device using an SH wave, whose frequency variation with temperature is 254 ppm in a temperature range from −40° C. to 90° C., exhibiting a lower frequency temperature characteristic than that of the foregoing ST-cut quartz. The device uses tantalum or tungsten having a density higher than that of aluminum as an electrode material to improve the frequency temperature characteristic. However, this has the problems of increasing electrical ohmic loss to further decrease the phase velocity.
The resonator according to Patent Document 2 uses an AT-cut quartz substrate whose thickness is smaller than the wavelength of an acoustic wave by five wavelengths, so that it has an excellent frequency temperature characteristic, thus providing for high frequencies. However, Nonpatent Document 2 exhibits a secondary temperature coefficient equal to that of the foregoing ST-cut quartz, and a frequency temperature characteristic of 320 ppm in a temperature range from −40° C. to 90° C., which is not better than that of the ST-cut quartz with low satisfaction.